請繪圖解釋良好點估計量(point estimator)的三種性質:不偏的(unbiased)、有
效性(efficiency)和一致性(consistency)。
請解釋stratified random sampling、cluster sampling、systematic sampling、
convenience sampling、judgment sampling 的作法及其使用時機(可舉例說
明)。
研究所入學考的平均統計學成績是47 分,歷史資料顯示,母體標準差可以假定
為10 分。今學校欲抽選樣本用以檢驗當年度的統計學入學成績是否有改變。檢
定的顯著水準為0.05。
(1) 請建立虛無假設和對立假設。(2%)
(2) 假設今年抽樣的樣本數是100 人,平均成績是45 分。請問,母體平均成績
的95%信賴區間的估計值為何?(4%)根據此信賴區間進行檢定,你的研究結
論為何?(2%)
(3) 請問此次抽樣結果所獲得的p 值為何?(4%)
(4) 假設今年實際上考生的統計學平均分數為46 分,學校希望有98% 的機會得
到的結論是:今年學生統計學成績下滑。若檢定的顯著水準為0.05,請問應
該用多大的樣本?(6%)
(5) 用上述的樣本大小做為評估基礎。若實際的統計學平均分數為46 分,請計算
發生型II 錯誤的機率為何?(2%)
下表為加州四個都會區的辦公室使用率。此份資料是否顯示辦公室的空屋率與都
會區相互獨立?令α = 0.05,你的結論為何?
Small cars get better gas mileage, but they are not as safe as bigger cars.
Small cars accounted for 18% of the vehicles on the road, but accidents
involving small cars led to 11,898 fatalities during a recent year (Reader’s
Digest, May 2000). Assume the probability a small car is involved in an
accident is .18. The probability of an accident involving a small car leading
to a fatality is .128 and the probability of an accident not involving a small
car leading to a fatality is .05. Suppose you learn of an accident involving a
fatality. What is the probability a small car was involved? Assume that the
likelihood of getting into an accident is independent of car size.
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